The hosts came into the encounter after four straight victories in all competitions, including a 4-2 win over Lille to end a six-match winless run in this tournament, and they were brimming with confidence in the first period.
Admittedly, they should have been behind inside 10 minutes when Jamie Leweling’s attempt hit both posts before bouncing away to safety, but their intensity caused Stuttgart all sorts of problems.
Shortly after, Gala took the lead through Alexey Batrakov, who hammered into the roof of the net when the ball fell to him.
Leweling had another chance to score from a similar position to his earlier miss, but he couldn't hit the target once again, and Gala soon made him pay as they doubled their advantage.
Once again, Batrakov was the goalscorer, running onto a delightful Davinson Sanchez ball into space before slotting between Fabian Bredlow’s legs.
Batrakov had a hat-trick chance midway through the half as Okan Buruk’s men had Stuttgart on the ropes, but Bredlow was equal to it on this occasion.
Stuttgart came close through Chris Furhrich with half-time approaching, but they struggled to match their opponents’ ferocity, which boiled over at times and led to handbags.
The game's high pace continued after the restart, with Victor Osimhen striking straight at Bredlow.
Fuhrich, Stuttgart’s most dangerous player, then hammered past the post, before Osimhen did the same at the other end.
Remarkably, Die Schwaben’s first shot on target didn’t come until the 58th minute, when Ugurcan Cakir comfortably collected a low shot from Bilal El Khannouss.
The Turkiye shot-stopper was soon tested by a far more threatening attempt, though, as he got two strong hands to a Deniz Undav effort from outside the area.
As the half progressed, Galatasaray dropped deeper, with Stuttgart desperate to find a way back into the game.
They thought they had halved the deficit through Fuhrich, who sumptuously curled into the bottom corner from 20 yards after Undav’s shot had cannoned back off the crossbar, but the latter was offside when receiving the ball and the goal was therefore disallowed.
Stuttgart came into the game with injuries to key players, such as Angelo Stiller and Josha Vagnoman, and they ran out of steam in the closing stages, although Cakir needed to make an important stop to deny substitute Dzenan Pejcinovic.
Therefore, Galatasaray saw out the game and made it successive Champions League wins, moving into the League Phase’s top 24 in the process.
Sebastien Hoeness’ men, meanwhile, lost their first game of the competition this term and became the first German side to suffer defeat away at Galatasaray since 1992.
Flashscore Man of the Match: Alexey Batrakov (Galatasaray)
